Title:
Estimating Treatment Effects using Multiple Surrogates: The Role of the Surrogate Score and the Surrogate Index

Abstract: Estimating the long-term effects of treatments is of interest in many fields.
A common challenge in estimating such treatment effects is that long-term
outcomes are unobserved in the time frame needed to make policy decisions. One
approach to overcome this missing data problem is to analyze treatments effects
on an intermediate outcome, often called a statistical surrogate, if it
satisfies the condition that treatment and outcome are independent conditional
on the statistical surrogate. The validity of the surrogacy condition is often
controversial. Here we exploit that fact that in modern datasets, researchers
often observe a large number, possibly hundreds or thousands, of intermediate
outcomes, thought to lie on or close to the causal chain between the treatment
and the long-term outcome of interest. Even if none of the individual proxies
satisfies the statistical surrogacy criterion by itself, using multiple proxies
can be useful in causal inference. We focus primarily on a setting with two
samples, an experimental sample containing data about the treatment indicator
and the surrogates and an observational sample containing information about the
surrogates and the primary outcome. We state assumptions under which the
average treatment effect be identified and estimated with a high-dimensional
vector of proxies that collectively satisfy the surrogacy assumption, and
derive the bias from violations of the surrogacy assumption, and show that even
if the primary outcome is also observed in the experimental sample, there is
still information to be gained from using surrogates.